Superphylum Deuterostomia Grobben, 1908 - deuterostomes see Infrakingdom Deuterostomia Grobben, 1908
   Phylum Chordata Bateson, 1885 - chordates
     Subphylum Craniata auct.
       Infraphylum Vertebrata Lamarck, 1801 - vertebrates
         Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
           Eugnathostomata
             Grade Chondrichthyomorphi [monotypic]
               Class Chondrichthyes Huxley, 1880 - cartilaginous fishes
                 Subclass Holocephali Bonaparte, 1832
                   Superorder Holocephalimorpha Lund, 1986
                     Cochliodontomorpha
                       Order †Cochliodontiformes Obruchev, 1953
                         1 Family †Cochliodontidae Owen, 1867
                         2 Family †Psephodontidae Jaekel, 1898